Treffer: ANALYZING THE RELATIONSHIP BETWEEN UNDERGRADUATE STUDENTS' COMBINATORIAL THINKING AND COMPUTATIONAL THINKING.

This study aims to analyze the relationship between undergraduate students' combinatorial and computational thinking through combination tasks solved in programming settings. Tasks in combinatorics have generally involved understanding the context of problems accurately. However, undergraduate students often find it difficult to come up with ideas when solving contextualized combinatorics problems. Lockwood et al. (2020) showed the potential of teaching and learning of combinatorics by analyzing undergraduate students' combinatorial problem solving in programming settings. Exploring undergraduate students' thinking during combinatorial problem solving in programming settings can contribute to the discussion of a deeper understanding of concepts in combinatorics. Seven undergraduate students participated in this study. Students were given tasks that can be solved by permutation with repetition or combination and asked to solve them by both handwork and coding in Python. We applied Lockwood's (2013) model, which frames students' combinatorial thinking in terms of formulas/expressions, counting processes, and sets of outcomes. In the programming context, we questioned students about the patterns of the code regarding variables, conditionals, and loops. We further questioned students about the relationship between the handwork and corresponding programming code to analyze the relationship between combinatorial and computational thinking. Students first enumerated all possible cases by hand. Considering all the cases, students formed a set of outcomes and formulated a formula for permutation with repetition. Then, by reorganizing and recounting each element of the set of outcomes, they derived a combination-based formula that led to the same solution. Students constructed the programming code based on the set of outcomes that they had formed by hand. The final codes were completed based on students' ideas using combinations rather than permutations with repetition. The programming settings helped students to understand the connection between permutation with repetition and combination. [ABSTRACT FROM AUTHOR]

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